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A356015 a(n) = n! * Sum_{k=1..n} 1/(k * floor(n/k)!).

%I A356015 #13 Aug 12 2025 02:51:27
%S A356015 1,2,6,21,125,625,5089,38185,343657,3376081,40765681,427649761,
%T A356015 6038448481,84486386881,1252766088001,19388604009601,350529058051201,
%U A356015 5938944734419201,119242323659692801,2303746722596390401,48358406991122726401,1063884813011759692801
%N A356015 a(n) = n! * Sum_{k=1..n} 1/(k * floor(n/k)!).
%H A356015 Vaclav Kotesovec, <a href="/A356015/a356015.jpg">Plot of a(n)/n! for n = 1..10000</a>
%F A356015 E.g.f.: (1/(1-x)) * Sum_{k>0} (1 - x^k) * (exp(x^k) - 1)/k.
%F A356015 Conjecture: a(n) ~ c * n!, where c = 0.95488757... - _Vaclav Kotesovec_, Aug 11 2025
%t A356015 Table[n! * Sum[1 / (k*Floor[n/k]!), {k,1,n}], {n,1,25}] (* _Vaclav Kotesovec_, Aug 11 2025 *)
%o A356015 (PARI) a(n) = n!*sum(k=1, n, 1/(k*(n\k)!));
%o A356015 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (1-x^k)*(exp(x^k)-1)/k)/(1-x)))
%Y A356015 Cf. A355987, A356011.
%K A356015 nonn
%O A356015 1,2
%A A356015 _Seiichi Manyama_, Jul 23 2022